Not a fan of new digital scopes. Four reasons I won't buy one as an amateur:
1. Reliability. Check eBay. Every cheaper second hand one I've seen has dead channels/amps. Doesn't matter if its Rigol or LeCroy or anything inbetween.
Sorry but that is complete nonsense. Aside from the fact that there are tons of fully working DSOs on ebay as there are broken analog scopes, just because there are X number of scopes on offer with a dead channel doesn't mean you have the tiniest clue about how reliable this particular scope is simply because you know nothing about the number of scopes out there that are working fine and hence aren't sold for scrap.
You could similarly reliable results from reading in fish guts.
And btw, channels rarely go dead by themselves, usually it's users overloading them. Many better DSOs have switchable 1M/50ohms inputs which in 50ohms mode are usually limited to 5V or so. Usually there is overvoltage protection but that can't prevent excessive overloading.
And it's not that dead channels are unheard of with analog scopes.
This leads on to...
2. Complexity. The things are basically a small analogue front end, an FPGA and a computer. Also its all SMD devices and difficult to repair. Channel gone? Good luck fixing it out of warranty without a rework station and an expensive Farnell order (if you can actually get the parts in that small volume). Maybe aliexpress has the part: 29 day lead time...
You obviously have never had the joy of finding one of the obsolete proprietary parts for certain analog Tek scopes. This aside, most analog scopes contain lots of components like mechanical switches and potentiometers that don't age well, and in case of the switches fixing them or finding working replacements can be a real pain in the arse.
Modern DSOs, even cheap ones like the Rigol DS1054z that is often recommended to beginners, have the capability to easily exceed the lifespan of most analog scopes, because there are less components under mechanical stress, and ageing is compensated by self calibration routines.
3. Crippleware. The hardware of the cheap stuff is capable but to tier the devices so you can pay for what you need and they can sell a small selection of base hardware configs, so you have software licenses to deal with. Or in the case of Tek, expensive feature modules that don't do anything other than switch a feature on. I think Rigol do this with license keys. Buy a Ferrari, find its limited to 60mph, then spend another $6000 on the 1000mph upgrade? Nope - no thanks.
Well, like in most cases, car analogies are just silly. Of course it's price gouging by selling software unlocks, and it's debatable if it's morally ok (legally it certainly isn't) to circumvent the software locks, but staying with an analog scope that can't do shit while even the most basic DSO without any of the software options unlocked outperforms the analog clunker easily just because of the existence of software options is silly, really.
4. Trust. The first thing my electronics lecturer said to us at university was that "all equipment tells fibs and lies". To have vast swathes of information presented to you relies on certain algorithmic and mathematical assumptions which aren't really well documented.
If your lecturer really belives this then maybe he should better stop teaching and go back learning the basics then, because the algorithms used in DSOs are pretty fundamental knowledge of signal processing, and there are swathes of documentation available if he could be bothered to do some research.
Coming from a professional software/math background this is a surprisingly complex and error prone area. There are as many rules as your average analogue scope there to consider. To package this up in something entirely trustworthy isn't possible. Perhaps 90% accurate but that's short enough not to want to make any assumptions about.
Any test instrument lies, that's a fact. Digital scopes lie, even if used properly. How much they lie is declared in the specs, which if the scope is working fine and used appropriately are completely reliable. Analog scopes lie, too, but in addition they often age worse than digital scopes, and then there are external factors like the user having to read from a scale (which often introduces even more errors) and guestimating the value, while DSOs (if properly used) present you with a measured value that is correct within the constraints of the scope's specification (which for DSOs are regularly magnitudes better than for analog scopes).
What makes a good engineer is being able to deal with the uncertainties of a test instrument instead of simply avoiding to deal with them alltogether.
A fine example is determining the frequency of a complex wave isn't as straightforward as it makes it out to be, even with an FFT in front of it and a tick on the feature list.
It is, if you're aware that you'll only see a segment of the frequency spectrum and that frequency components below a certain amplitude aren't shown, and that's not a problem.
That's where being an engineer comes into play, if you don't know the basics then a DSO won't help you to vercome your lack of basic knowledge.
In addition an analog scope won't tell you anything. The signal may look like a sine wave but in reality it's unlikely to be the case, and the analog scope won't tell you that there are other frequency components in the signal.
If I was doing it professionally I would buy a new DSO. Then write it off as operating expense when it dies but as an amateur the investment is a bit of a problem.
Not really. Even most cheaper scopes come with 3yr warranty, and most big brands allow you to extend that (some even let you buy manufacturer warranty for a 2nd hand scope you bought from ebay as long as it isn't too old and the factory seal is still in place, i.e. LeCroy).
On the other hand, the $150 you might pay for an analog clunker can quickly turn into a write-off if the CRT goes or any of the hybrids or other unobtainium parts.
Now count in the generally higher reliability of DSOs and the case for sinking money in an analog scope becomes even more unconvincing.