I could write a dissertation on the differences, and this topic comes up a lot, and lots of people have lots of strong feeling about it but in general
Positives of CRTs:
CRTs are what most of these games were designed to be played on, so they look and play best on these screens. Arcade CRTs generally look great, and they have 0 lag. These displays are designed for RGBs signals and games typicall run in progressive scan, so the picture quality is a lot more vibrant and precise than what you may remember from your old Tube TV. they're also available in large sizes in 4:3 aspect ratio.
The absolute fastest LCDs on the market have 8-16ms of lag (1/2 to 1 full frame) where most good consumer level displays have 24-32ms of lag (1.5 to 2 full frames). almost none of them are capable of displaying the low resolution content from arcade boards so you need a converter. Crappy converters add even more lag and scaling errors. If you want good conversion with scanline emulation you'll need something like the OSSC which is nearly the price of a used CRT itself. Also almost no LCDs over 19" exist in a 4:3 aspect ratio so you'll be playing 4:3 games on a 16:9 screen so 99% of it will be black barred.
Positives of LCDs:
LCDs are still made so you can buy them new and will be able to for the foreseeable future, even used arcade grade CRTs are still relatively new so they typically have some good life-span ahead of them still. In general they're not going to give you any maintenance or replacement headaches. They're a lot lighter and easier to move around. In general an LCD candy will be a lot more comfortable in terms of the amount of control panel space you get since they tend to be a bit wider and you sit a bit further away from the screen.
CRTs by comparison are all old, even the newest ones. While the picture is great, that's generally only true if it's received a "rebuild" at some point in it's life, which is something that generally should be done every 10-15 years. Parts for some monitors are impossible to source, meaning that if it fails you might not be able to fix it and have to seek out another used chassis (the monitor PCB). They're also crazy heavy and the "neck" on the back is fragile enough that you could accidentally wreck the tube if you bump into it while working on it (it happens).
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Personally I'm a fan of using the most appropriate display for the particular game... if it was a CRT game I want to play it on a CRT, if it was an LCD I want to play it on an LCD. I don't mind putting in the effort to keep CRTs going.
CRTs aren't necessarily inexpensive. Most used Arcade CRTs chassis like those in Candy Cabs sell for $150-$300, can be hard to find and might still need to be rebuilt. rebuilds yourself can cost about $40 or $150-$200 if you have someone else do it. "NEW" CRTs that are still kicking around can cost up to $650. if you can manage to find one.
LCDs in general can be had for much less, but an arcade quality, low lag display, plus GOOD conversion equipment can easily run $1000-$2000
If you do want to entertain getting an LCD cab (Taito Vewlix, Sega Lindbergh, Namco Noir, or Delta 32) speak to Jassin as he's the resident LCD fanbo... I mean Expert
Buy IMO it basically boils down to:
"low cost", authentic experience, low maintenance ... pick two
