It depends.
What will the NIC be used for? Most people here (I think) use 2 NICs, one for the camera network and one for the LAN network. For the camera network, you probably would not benefit. I am running 16 cameras (I think) and I am nowhere near to even utilizing 1Gb for the camera network.
If its for the LAN side, a 2.5Gb NIC will be very useful, as you can then export clips 2.5x faster than before (Or a little under, as most modern hard drives can read at around 200MB/s which is 1.6Gb/s) and it also means you won't be maxing out the link when exporting video. Of course viewing the cameras is using bandwidth, so if you have 4 people viewing UI3 and exporting a video, the 2.5Gb NIC will be useful.
But, will you have a 2.5Gb switchport to connect it to, so will it link at 2.5Gb? Either way if the NIC is cheap enough, just go for it. However, if the 1Gb NIC is Intel and the 2.5Gb is Realtek etc, go the 1Gb Intel. Quality over speed!
I have a 10Gb connection for my BI Machine
If it’s the same cost go for it but it probably won’t make a difference; your bottleneck will be your hard drive and file system.
File system has nothing to do with it, and most hard drives can easily max out a gigabit link
If you are talking on you physical lan ie lan interconnections. Until you update the switches it wont matter unless you are using LAGG. Since I doubt LAGG is need it would just auto negotiate down to the speed of the connection on the other end. If you are connecting BI directly to the router it might help interconnection speed but that is about all. Plus most cams are 100 Mbit anyway.
Also as an aside unless you have a internet plan above 1 Gigabit . The 2.5 nics dont help there either.
You internet has nothing to do with local network speed, else my 25Gb SFP28 and 40Gb QSFP+ connections would be useless!