I agree with Spidey ftw; but your reasoning sounds backwards to me.
Beast's strength was amped years ago- I believe he is much stronger than Spidey now, and certainly Spider-man is MUCH faster and more agile.
No one can agree how strong Beast is. He is however a better trained fighter, with an expert knowledge of pressure points.
I doubt there's much to choose between them in terms of agility, but Spidey is certainly faster.
Beast has claws, hyper senses, a longer reach, and is a super-genius.
Spidey has the spider sense and the webs, and is also a genius, but not on Beasts level.
Unfortunately Beast just doesn't have enough good showings to suggest he'd win this.
Spidey has the agility of a spider. Beast has been described as having the agility of an ape.
Back in Secret Wars, Spidey proved he was much more agile than Nightcrawler... perhaps it was an inaccurate assumption on my part, but I thought Nightcrawler was about on par with Beast in agility.
In an Avengers comic featuring the High Evolutionary, Hulk and Hercules are unable to bend bars until Beats adds his strength to the situation. Hulk comments on the increase in Beast's strength level- I don't know what the extent is, but I figured it must be significant if the Hulk noticed.
Isn't Spidey's exceptional reaction speed among the fastest mortal heroes? Isn't it a given that he is faster than beast?