CBSpeccy is the fastest 128k for up to 030 machines and supports Pentagon timings, usefull for demos with pentagon-specific timings. ZXLive is also good and still under development. X128 is very compatible , but slow for anything below 060. ZXAM is very good and feature rich, but only supports 48k + AY chip music. The king of the hill, and really, you need to look no further if you have 040+ machine, is ASp. It pretty much runs anything you throw at it, it emulates everything usefull a real Speccy had and it's still under development so you may send your ideas to Ian Greenway (the author) for improvement.
In conclusion, if you're on 040+ machine go for ASp. If you need pentagon timings and some other unique stuff go for CBSpeccy. If you're on 030 or less, CBSpeccy again, but install ASp as well as it's more compatible with certain programs and with some good tweaking it runs very decently on 030@50+AGA. If you get hold of a previous version of ASp, can't recall the exact version, was it 0.77 or maybe even earlier? Anyway, what I was saying, with that version ASp uses a direct AGA screen which is very fast on 030 and less. You may ask the author directly for that version. IMO install both ASp and CBSpeccy, you'll find yourself using ASp most of the time if you're on 040+, but CBSpeccy may be handy for some weird stuff you may come across. It's the other way around if you're on 030 or less.