What are some primary grammatic differences between American and British English?

Question

Not in terms of spelling, but of sentence construction...I believe they use the gerund more often...?

Answer 1

I don't think sentence structure is too much different.  I tend to use gerund often, myself.

I think spelling, pronunciation, and slang are all different.

Such as, Americans write realize where British write realise. :)  

Answer 2

Taivo already has some great examples.  I'll just add a few more I can think of.

We Americans tend to use the Simple Past with adverbs like just, already, and yet.  The British tend to use the perfect tenses instead.

American: I already ate.

British: I have already eaten.

Americans also continue to use the past participle "gotten" for the verb "get," which has been merged with "got" in British English.  In American English, using the past participle "got" generally indicated ownership, while the past participle "gotten" is generally used for receiving or becoming.

American:  He has gotten much better.

British:  He has got much better.

Some prepositions are used a bit differently.  In American English you play "on" a team, while in British English you play "in" a team.  In American English you live "on" a street, while in British English you live "in" a street.

That's all I can think of right now

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The article I quote in my sources gives some "differences" in "gerund vs. to+infinitive" usage, but I'm not convinced that there are any absolute differences.

For example, inferring from what the article says something like this would be true:

American:  He began talking.

British:  He began to talk.

Answer 3

There are a number of past participle differences (the first form is British, the second American):  burnt/burned, dwelt/dwelled, learnt/learned, spoilt/spoiled, dreamt/dreamed, knelt/kneeled, etc.

The derivational suffixes -ify and -ize are more common in American English:  citify, burglarize, etc.

Using a noun for a verb is more common in American English:  an author/to author, a host/to host, etc.

Shall is virtually extinct in American English:  I shall tell you later (British), I will tell you later (American)

'would' can be used in a hypothetical sentence in American English:  I wish I would have done it (American), I wish I had done it (British); If I would have seen one, I would have bought it for you (American), If I had seen one, I would have bought it for you (British)

'ought to' is generally not used in questions in American English:  Ought we to eat that? (British), Should we eat that? (American)

There are dozens more differences, but the gerund is not one of them.  Gerunds are equally common on both sides of the Atlantic.