I've created a very rough little statistics comparing fighting events between the Matrix fight and the Reloaded fight.
It lacks some very significant details but can give you a picture nevertheless. Also it's quite demanding even to watch these fights for analysis so there are some errors for sure, but they don't alter the "big picture". "M." means Morpheus
event/Movie: TM RL change
M. attacks: 13 to 45, 346%
M. defends: 32 to 31, 100%
(combined: 45 to 76, 170%)
M. evades: 5 to 4, 80%
M. blocks: 12 to 13, 110%
M. hits: 8 to 22, 275%
M. gets hurt: 23 to 25, 110%
M. misses: 5 to 18, 360%, of attacks: 38% to 40%
Note: of course you shouldn't believe no pretty
Matri tables! You need to see the thing for yourself!
What is interesting here is that, as you can see Morhpeus is not too much better in doing defense once he needs it. But he became so much more agressive and able in initiating attacks.
It can be that he is faster because of his mind and/or that he has learned important things, ways and skills about fighting Agents.
In terms (primarily*) of skill, it is natural I think that Neo tried to teach them as much as he can (shamelessly linking here my previous answer).
But for the mind, it is also very-very important what also A Pale Shadow is saying in his answer, that Morpheus is believing in himself here.
Morpheus is basing his life on the Prophecy. He is called crazy (by Zee) and all, he is totally into it. In The Matrix, Morpheus saw his purpose as to buy time for Neo. So his own life was not conflicting with the Prohephecy. He succeeded in buying time.
In Reloaded, Morpheus understands that if the keymaker dies Neo cannot fulfill the Prophecy. He believes that the Prophecy will be fulfilled and this gives him the strength to believe in himself. I think this "further" frees his mind, allowing him to be faster, just as it was the case with Neo's in The Matrix.
Also, I know from experience, it really means a lot if you've seen/experienced something done, contrasted with when you only think that it "should" or "may" be possible, like defeating Agents here; and thus also agree with A Pale Shadow in that this definietly puts Morpheus in a more confident situation than in The Matrix.
Previously what they were thinking about agents was to run. Now he may think that they can be beaten if they are not fast enough. Quite a difference.
Also, do not forget that Morpheus at this point is actually experienced with fighting Agents!
As for Trinity, she can actually keep up relatively well. She never fought Agents before! Actually, if you check it, she falls for the same tricks as Morpheus at the first time (with Smith) - quite interesting! But she is also doing a bit better than Morpheus for the first time.
The real problem for Trinity actually only starts when there are suddenly two Agents.
Until that, she can actually keep up. (Not totally well, but she stands a chance, she has meaningful options available for her.) Only then, she starts to lose instantly.
*:(As a matter of fact I believe Neo also helped/trained Morpheus (and Trinity), in their mind field, as much as he could in the time prior to Reloaded. It would be hard to verify this, but even without doing so, the other things already provide some explanation.)