The Galaxy S10 Plus and Note 10 Plus are both powered by the same Snapdragon 855 chip from Qualcomm. Both phones also have an under-display fingerprint reader, wireless charging, use USB-C for power, and have stereo speakers (although YouTuber Marques Brownlee says the Galaxy S10 Plus actually has superior sound, in his opinion, compared to the Galaxy Note 10.)
When it comes to random-access memory, or RAM, which helps computers multitask more quickly, the Galaxy Note 10 Plus has 12 GB of RAM while the Galaxy S10 Plus comes standard with only 8 GB of RAM. You can upgrade to 12 GB of RAM in the Galaxy S10 Plus, but it's really overkill.
So, in general, expect these phones to perform about the same, despite their differences.