Not sure how far back you're going, or which model of Cisco router you're referring to. I first cut my teeth on networking working at a Tier 2 carrier back in 2005 on Cisco GSR's (12000 series) which use a 200MHz R5000 MIPS CPU, but they were already quite long in the tooth at the time and were one of the few remaining networks still running them. And I do recall implementing ACL's to be an issue. Not sure if you were referring to ACL's or BGP policies themselves when referring to securing BGP.

These days, a full BGP capable router starts with the ASR1001 for Cisco which starts with a 32bit 1.5GHz CPU + 4GB RAM on the RP1 and goes up to a 64bit quad-core 2.2GHz CPU + 8-64GB on the RP3. Juniper land, the lowest end non-EOS router would be the MX80 which comes with a 1.33GHz PPC CPU and 2GB RAM, but unofficially Juniper will always steer you towards the MX104 with a 1.8GHz CPU and 4GB of RAM. I can't comment on the ASR's, but we have MX80's and we can do line rate ACL's with hundreds of terms in ASICs without issue. BGP policies themselves are still handled by the CPU though, and are indeed quite slow on the MX80's with full convergence taking up to 20 minutes or so. We've mostly relegated them to core switching duty at this point though, and are waiting for the new MX204's (800Gbps in 1U) to become mature enough before replacing them.

Moving up a bit, we use MX480's as well which we currently have routing engines with 2GHz Intel CPU's and 4GB of RAM, which I believe these are already EOS, but not enough of an issue for us to buy upgraded routing engines for this platform. These do full table re-convergence in about a minute or two. I believe quad-core 1.8GHz is standard now though, with up to hex-core 2GHz available. I don't think CPU's are really much of an issue anymore, although obviously still not as fast as what you can find easily enough in commodity hardware. The ASICs handle most things flawlessly though.