Quite a difference to not much depending on pedal and reverb plugins being compared.
Which probably isn't a very helpful answer :-)
Having said that, delay and reverb are related but very different things. And "ambient" covers a wide range.
For what it's worth I have a variety of delay pedals collected over the years (decades even). If I'm tracking guitar and want anything more complex than a Deluxe Memory Man can do I tend to use delay plugins, and even then I might well use a plugin. The advantage the plugins have is the settings are retained when the project is saved, so you can always get the settings back if you decide to track some more or need to punch in later.
While it's true that a delay plugin isn't quite the same as a good analogue delay like the DMM or MXR Carbon Copy, plugin delays like Boz Digital's one can do things no pedal can, and you can have as many instances of a plugin as your cpu can stand.
As for digital delay pedals, the TC ones sound very good in my opinion, Boss not so much and Line 6 even less. TC's delays you can sync to the DAW with MIDI are a very good idea.
I don't seem to play live much these days, but when I do I use pedals, often a Boss Dd-20 which isn't my favourite but has useful memory functions, and unless the tempo is fixed by a sequencer or drum machine tap tempo is essential in case delay time needs to be adjusted because the band's timing has slipped. Plus a Carbon Copy set to low feedback and delay time of around 300ms as a "thickening" delay.
The short answer is that analogue bucket-brigade delays don't sound like the digital or software "analogue" delays, but are more limited in what they can do. Tape delays are expensive, need maintenance and are generally a nuisance to deal with.
As for reverb, for ambient stuff where I'm recording using a Sansamp, I like Overloud's Springage. Not quite the same as my Fender valve reverb unit but still impressive. Also the reverbs that come with Sonar, all of which are good. I've no experience of reverb pedals because my Fender unit covers anything I'm likely to want to run with an amp.