And major difference is eglot is slimmer compared to lsp-mode, integrates with and relies on built-ins more (xref etc) rather than inventing its own paradigm, is less cluttered by default and IME less buggier than lsp-mode cludge and now comes with emacs so doesn't need any other packages (other than language servers themselves, of course).
OTOH lsp-mode supports more than 1 active language server per buffer, generally support more features of the protocol than eglot and installs servers automatically (which may be a feature or bug depending on your system).
It comes down to utility and personal preference, but I've used lsp-mode before, found it quite buggy and cluttered, moved to eglot and have near zero LSP config now.