Well, I think it will be tricky trying to get them more or less identical, unless you can use the same filter. Inkscape has Filters menu > Non-realistic 3D Shaders > Chrome, and Chrome dark. I have found them extremely lacking when used on text or text-like objects, like parts of your logos. But they would certainly be worth experimenting.
And definitely if you're skilled with the Filter editor, you could create your own filter, or perhaps recreate the PS filter. (I've recently dived into learning the Filter editor, and find it extremely challenging.)(But once I get it figured out, I think will be really fun

) There's also Filters menu > Bevel > Button. Also not very applicable to text, but maybe on your green oval would work better? Definitely worth a try.
Other than that, I think just skilled and precise use of gradients and blurs, would be needed. Sorry, I wish I could be more helpful....but surely other people will have more ideas?