The simplest way is to go by your Dutch or German intuition and to forget all about English. Kidding aside (unless you happen to speak Dutch), you would always say courir est très ennuyeux, because the other construction just isn’t a thing.

As an aside, do you mean tiresome as in boring and tedious (which I’m quite sure is the primary meaning of ennuyeux) or tiresome as in physically wearying (probably fatiguant)? With that, on to the question:

• You use the gérondif to express an action that takes place at the same time as the principal verb. (I am working while listening to a symphony = Je travaille en écoutant une symphonie.) In this usage the subject of the gérondif has to be the same as that of the principal verb.
• It can be used adverbially[1] as a complément circonstantiel (CC) when preceded by en:
  • simultaneity. In this usage the CC is often preceded by tout, as in “Ce plan offre de nombreux avantages tout en minimisant la perte d’actifs.”
  • cause
  • manner
  • hypothesis
  • concession
• periphrastic aller + gérondif (without en)
  • Son mal va s’aggravant (= continue de s’aggraver).

Source: Anne Struve-Debeaux, Maîtriser la Grammaire française, 2010, 3.III.2, p. 217.

Also see: http://french.about.com/od/grammar/a/presentparticiple.htm

[1] While minimizing loss of assets is an adverbial clause. Just picking a tiny nit. 😉

It all depends on the sentence’s construction. Here in your first sentence

Courir est très ennuyeux

you could rephrase it as

Il est très ennuyeux de courir

So the use of the use of the verbal form is just because you switch words in the sentence.

In your second sentence, the correct form is the second one, and it all comes from the en meaning that you have to use the gerund form.

Ce plan offre de nombreux avantages tout en minimisant la perte d’actifs.

Edit : as @MorganFR said, watch out for some sentences where ‘en’ can have a different meaning

J’ai trop de bonbons, j’aimerais en donner.

Double check if you can change the ‘en’ with another word, like here

J’ai trop de bonbons, j’aimerais donner [ces bonbons].

Easy trick that work most of the times : If you can replace your -ing verb with "to [verb]", you’ll use an infinitive.

Note that there are other possibilities than the two you mention. Here’s how it works :

Running is very timesome.

To run is very tiresome

(It’s not the best way to say it but you get it)

-> Courir est ennuyeux

He likes to drink while he is running

He likes to drink while he is to run

It doesn’t work, you can’t translate with an infinitive. In that case you need a gerund :

Il aime boire en courant

But more generally, you typically use a gerund when you’re using "while" or "when".

The other cases I can think of is "running" being translated to "en train de courir", or when it’s an adjective or a noun it’s also different ("a running session",…)