You will get different answers because it is a matter of personal taste and just as many prefer a certain item canned as frozen. It also depends on if you have a pressure canner as many things on your list require pressure canning.

Personally I would never can broccoli, frozen only. Spinach can go either way tho I prefer canned a bit. Rutabagas and beets - canned only. Peppers and onions - frozen. Tomatoes canned. Have no use for parsnips, sorry. ;)

Dave

For what it's worth, here's my personal experience:
Broccoli - frozen.
Spinach - frozen.
Rutabaga - I just buy those as I need them, so can't help you on that one.
beets - canned.
sweet peppers - surprisingly, they are great frozen. I just thawed some and used them in a stir fry. Couldn't tell the difference between the frozen ones and fresh ones. I do can hot peppers (to substitute for grocery store "canned green chilis").
tomatoes - Depends on the use. I can whole and diced tomatoes and salsa. I freeze prepared sauce.
onions - I keep them in the root cellar or, if they are sweet ones, in the refrigerator. Frozen is OK, but my freezer smelled for months until I totally cleaned it out (double or triple wrap those puppies!)
parsnips - I have successfully frozen 'snips I've gotten at the grocery store. They get a little soft, but they're great roasted or in soup.

Broccoli, spinach and peppers freeze great for me
My first year freezing a few tomatoes so I don't know the results yet

I'd freeze broccoli, spinach (though canned is fine) and peppers. I have canned peppers (and of course pickled or relishes are very good canned). But I prefer frozen. I freeze chopped sweet bells for use in recipes, stuffed peppers (unbaked), and piperade (peppers, onions, tomatoes, sauteed with olive oil, paprika, smoked paprika, sherry vinegar, etc.).

Beets I can, both plain and pickled.

Tomatoes are both canned (pasta sauce, spaghetti sauce with meat, crushed and whole, roasted tomatoes in soup) and frozen (gazpacho, tomato soup base, roasted in olive oil, dried with an olive oil and herb baste) depending upon the recipe and the use.

Rutabagas, onions and parsnips are neither frozen nor canned. Onions are dried and cured. Parsnips and rutabagas are cold storage (the garage). They keep very well if you have cool but not freezing conditions.

I am particularly a fan of parsnips, but I admit there are a lot of bad recipes out there.

Carol

I love parsnips, there's never enough to can because I eat them as fast as I can.

I can tomatoes, spinach, rutabagas, beets. I freeze or dry peppers and I dry onions. Broccoli I freeze, it's too mushy when canned.

Rutabagas do get a little "strong" when canned, but I don't mind that. Some people hate it, that's why they took the directions for canning out of the Ball Blue Book for a couple of years. It's back now.

Malna, I agree on the onions. I double bagged a bunch and my freezer still reeked of onion for months.

Annie

I agree that it's a matter of taste and how you use each of them.
I freeze:
Broccoli, spinach, onions (chopped), and peppers (chopped and halves for stuffing).
I can tomatoes (also sauces, salsa) and freeze them.
I'm not a big beet person, except pickled, so those are canned.
I don't grow rutabaga or parsnips, so no opinion there!

I say just try it! I sure wouldn't turn down the freezer!

Deanna

Broccoli...frozen only
Spinach...frozen prefered, canned ok
bell peppers...frozen, some chopped, some sliced lengthwise
onions...I keep either in my laundry room or in fridge. If they start to go bad, I chop & freeze. I've never had a smell in my freezer from them!
tomatoes...canned or fresh
beets...canned, I only like pickled
I've never done parsnips or rutabaga.

Eagles, I think that everyone said about the same thing. Try to get that freezer going and get some sweet peppers frozen, they are easy and available now. You will learn what freezes well and what is best canned or fresh over time. Next year, plan on freezing some blueberries- easy and very good all winter. Luke