Learn English – ‘they have’ or ‘the ones have’

Answer update for question marked "UPDATE (17th Feb 2014)":

Restricted between only the two options, the first one is preferred, and fixed grammatically (minimally) as follows:

• They can help you better. ("More better" is redundant. See Note below.)

A more idiomatic way of saying this would be one of the following:

• They can better assist you with this issue.
• They can assist you better.
• They can assist you better than I can. (very formal)

However, I would question why you need to defer to others as "better". It certainly depends on your manager and situation, but speaking for American culture, the following would probably be better:

• Good: To best serve you, I am referring you to level 2 support.
• Better: To best serve you, this ticket is being escalated to level 2 support.
• Best: To best serve you, this ticket is being escalated to level 2 support. However, if you have any concerns with your support level at any time, please do not hesitate to contact me.

Note that "more better" is redundant:

• = more [ better ]
  = more [ higher quality ]
  = more [(higher) quality ]
  = more [(more high) quality ]
  = more more high quality

OLD ANSWER BELOW
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1. Definitions

More help = Additional help in certain areas. Can imply better but not necessarily.
Better help = Improvement in one or more qualities of help (faster, more thorough). Can imply more help, but not necessarily.
Way = Specific methods used.

2. Try to identify your needs in terms of the following:

1. "What is better?"
2. "More of what?"
3. "By what method (way)".**

3. Examples:

• Even though the new guy doesn't have the same depth of knowledge in SQL Server Management, the new guy can help you more to get your business going. (The new guy has a wider skill set and that's what you need. He's a better match for you in the opinion of the person saying this.)

• There's a guy I know that can help you better. (A little odd construction but ok in context in conversation.)

• There's a guy I know that can help you better with your taxes. (Sill odd but a little better.)

• There's a guy I know that can help you better prepare for your taxes. (Good. "better prepare" is a more specific "way" than "better with".)

• There's a guy I know that is better at icon design. I think he can help you more than the guy you have. = GOOD

• There's a guy I know that can help you more and better. = Bad

• There's a guy I know that can help you more with your website. He has more experience and better prices. In fact, his service is better too; he's company is on call 24/7! (VERY GOOD)

Here the verb "to take" is being applied to the noun "technology". In a much simpler form, the sentence would be

Technology takes advantage of (something)

This is still the correct form to use when additional qualifiers and elements of speech are included. Additionally though, I would point out that while many different components of many different cars have changed from mechanical to digital, you are really talking about a single change in the technology used to make cars. So I would say instead

The cars underwent a rapid change from the application of mechanical technology to digital, that currently takes advantage of artificial intelligence.

Edit: Another possibility, that makes one of your initial forms correct in this context, is to say

...that is currently taking advantage of...