I don't have a gigabit connection, so don't have any experience with it unfortunately, but I can't recall seeing any complaints about the built in port, the only problems I've seen reported have been with the asix drivers in the new tp-link adapter which seems to be limited to around 600mbps, maybe someone else can chime in.
Router on a stick means you have to use a single (onboard-) port for wan and lan, this works fine up to ~500 MBit/s (more like 750-800 MBit/s in practice, as you'll rarely experience fully symmetric up- and downstream usage scenarios), but to achieve the full 1 GBit/s up and down, you need dedicated interfaces for wan and lan (so not router on a stick).
To explain it simply, your (onboard-) 1 GBit/s ethernet card is fully symmetric - it can do 1 GBit/s up and 1 GBit/s down at the same time. For routing to work, the data passes through this single link twice - once in, once out, but the hardware can only do 1+1 GBit/s, not 2+2 GBit/s, which you'd need for a symmetric load for a router on a stick. This is not specifically an issue of the RPi, but a rather physical limitation of 1000BASE-T - you'd need at least 2.5GBASE-T (or 5GBASE-T, 10GBASE-T) to escape this (for practical reasons, two dedicated 1000BASE-T cards are just much cheaper than busting the 1 GBit/s limit).
tl;dr: don't worry, it will still work (with a slight performance impact), but you'd still want to get a second ethernet card exclusively for WAN.